1. Field of the Invention
The present invention generally relates to a bandgap reference circuit, which can successfully operate with a low supply-voltage below 1.25V, and more specifically to a bandgap reference circuit having a single stable operating point to avoid startup failure.
2. The Prior Arts
General high performance electronic circuits greatly need a stable reference voltage without suffering from different variations caused by the power source, loading level or operating temperature. For example, the reference voltage can be used as an input signal of a comparator to compare with another internal or external signal. The reference voltage is often generated by a reference circuit with complicated structure so as to block all the inevitable variations due to the power source, loading or temperature.
In the prior arts, electronic manufacturers have successfully developed many reference circuits which can prevent the influence caused by the power source and loading level. Additionally, the variation of the temperature is blocked by using a differential operational amplifier as well as resistors and diodes to assemble a specific circuit having both the positive and negative temperature coefficients, and in particular, the positive and negative temperature coefficients are signed to almost the same in the magnitude such that the temperature effect is greatly reduced. Specifically, the first and second orders of the temperature coefficient for the reference circuit are almost zero.
Please refer to FIG. 1. The bandgap reference circuit in the prior arts comprises a differential operational amplifier OP, a metal-oxide-semiconductor (MOS) P, a first resistor R1, a second resistor R2, a third resistor R3, a first diode D1 and a second diode D2. The reference voltage Vref is generated at the drain terminal of the MOS P, and the second diode D2 is implemented by several diodes connected in parallel and each identical to the first diode D1 in electrical property.
More specifically, the bandgap reference circuit is configured such that the output end of the differential operational amplifier OP is connected to the gate terminal of the MOS P, the source terminal of the MOS P is connected to the power source Vcc, the first resistor R1 is connected between the drain terminal of the MOS P and the positive end of the first diode D1, and the second resistor R2 and the third resistor R3 are connected in series between the drain terminal of the MOS P and the positive end of the second diode D2. Particularly, the positive end of the first diode D1 is further connected to the inverting input end of the differential operational amplifier OP, and the connection point of the second resistor R2 and the third resistor R3 is further connected to the non-inverting input end of the differential operational amplifier OP, thereby providing a feedback control loop.
The detailed operation of the bandgap reference circuit in FIG. 1 will be described as follows.
First, the current of the diode in accordance with the current-voltage characteristic is illustrated by equation (1):
                                                        I              =                            ⁢                              Is                ·                                  (                                                            ⅇ                                                                        q                          ·                          Vf                                                                          k                          ·                          T                                                                                      -                    1                                    )                                                                                                                                          ≅                                    ⁢                                                            Is                      ·                                              ⅇ                                                                              q                            ·                            Vf                                                                                k                            ·                            T                                                                                                                ⁢                    VF                                                  >>                                                      k                    ·                    T                                    q                                            ,                                                          (        1        )            where q is the electrical charge per electron (1.6×10−19 C), K is the Boltzmann constant (1.38×10−23 J/K), T is the absolute temperature, Is is the reverse saturation current, and Vf is the thermal voltage (26 mV at 25° C.). The thermal voltage Vf can be expressed by equation (2):
                    Vf        =                              V            T                    ·                                    In              ⁡                              (                                  I                  Is                                )                                      .                                              (        2        )            
Therefore, when the differential operational amplifier OP is operated at a steady-state, the inverting input voltage Va is equal to the non-inverting input voltage Vb, that is I1·R1=I2·R2, and the first current I1 and the second current I2 flow through the first resistor R1 and the second resistor R2, respectively. Thus, the following equations are obtained from equation (2):
            Vf      ⁢                          ⁢      1        =                  V        T            ·              In        ⁡                  (                                    I              ⁢                                                          ⁢              1                                      I              ⁢                                                          ⁢              s                                )                                Vf      ⁢                          ⁢      2        =                  V        T            ·              In        ⁡                  (                                    I              ⁢                                                          ⁢              2                                      N              ·              Is                                )                    and equation (3) results:
                                                                        d                ⁢                                                                  ⁢                Vf                            =                            ⁢                                                Vf                  ⁢                                                                          ⁢                  1                                -                                  Vf                  ⁢                                                                          ⁢                  2                                                                                                        =                            ⁢                                                V                  T                                ·                                  In                  ⁡                                      (                                                                                            N                          ·                          I                                                ⁢                                                                                                  ⁢                        1                                                                    I                        ⁢                                                                                                  ⁢                        2                                                              )                                                                                                                          =                            ⁢                                                V                  T                                ·                                                      In                    ⁡                                          (                                                                                                    N                            ·                            R                                                    ⁢                                                                                                          ⁢                          2                                                                          R                          ⁢                                                                                                          ⁢                          1                                                                    )                                                        .                                                                                        (        3        )            
The reference voltage Vref shown in FIG. 1 can be expressed by equation (4):
                                                        Vref              =                            ⁢                                                Vf                  ⁢                                                                          ⁢                  1                                +                                                                            I                      1                                        ·                    R                                    ⁢                                                                          ⁢                  1                                                                                                        =                            ⁢                                                Vf                  ⁢                                                                          ⁢                  1                                +                                                                            I                      2                                        ·                    R                                    ⁢                                                                          ⁢                  2                                                                                                        =                            ⁢                                                Vf                  ⁢                                                                          ⁢                  1                                +                                                                            (                                                                        d                          ⁢                                                                                                          ⁢                          Vf                                                                          R                          ⁢                                                                                                          ⁢                          3                                                                    )                                        ·                    R                                    ⁢                                                                          ⁢                  2                                                                                                        =                            ⁢                                                Vf                  ⁢                                                                          ⁢                  1                                +                                                      (                                                                  R                        ⁢                                                                                                  ⁢                        2                                                                    R                        ⁢                                                                                                  ⁢                        3                                                              )                                    ·                                      dVf                    .                                                                                                          (        4        )            
Subsequently, equation (5) is resulted in by combining equations (3) and (4):
                              V          ref                =                              V                          f              ⁢                                                          ⁢              1                                +                                    V              T                        ·                          (                                                R                  ⁢                                                                          ⁢                  2                                                  R                  ⁢                                                                          ⁢                  3                                            )                        ·                                          ln                ⁡                                  (                                                                                    N                        ·                        R                                            ⁢                                                                                          ⁢                      2                                                              R                      ⁢                                                                                          ⁢                      1                                                        )                                            .                                                          (        5        )            Vf1 in equation (5) is the built-in voltage, which has a negative temperature coefficient (−2.2 mV/° C.) and VT has a positive temperature coefficient (+0.085 mV/° C.). Further, equation (6) is derived by putting these parameters into equation (5):
                              V          ⁢                                          ⁢                      ref            ⁡                          (              T              )                                      =                              (                                          V                                  f                  ⁢                                                                          ⁢                  10                                            -                              2.2                ×                                                      10                                          -                      3                                                        ·                  Δ                                ⁢                                                                  ⁢                T                                      )                    +                                    (                                                V                                      T                    ⁢                                                                                  ⁢                    0                                                  +                                  0.085                  ×                                                            10                                              -                        3                                                              ·                    Δ                                    ⁢                                                                          ⁢                  T                                            )                        ·                          (                                                R                  ⁢                                                                          ⁢                  2                                                  R                  ⁢                                                                          ⁢                  3                                            )                        ·                                          In                ⁡                                  (                                                                                    N                        ·                        R                                            ⁢                                                                                          ⁢                      2                                                              R                      ⁢                                                                                          ⁢                      1                                                        )                                            .                                                          (        6        )            
Therefore, if the temperature coefficient of Vref(T) is zero, then
                    ∂        Vref                    ∂        T              =    0    ,
and equation (7) is thus obtained:
                                          (                                          R                ⁢                                                                  ⁢                2                                            R                ⁢                                                                  ⁢                3                                      )                    ·                      In            ⁡                          (                                                                    N                    ·                    R                                    ⁢                                                                          ⁢                  2                                                  R                  ⁢                                                                          ⁢                  1                                            )                                      =                  25.88          .                                    (        7        )            
At this time, Vf10 is about 0.6V, and VT0 is about 0.026V for the temperature 25° C., and equation (8) is derived from equations (6) and (7):Vref=0.6+0.026·25.88=1.27  (8).
From the above-mentioned, the bandgap reference circuit shown in FIG. 1 generates the reference voltage, 1.27V, regardless of the first, second and third resistors. That is, the reference voltage may suffer some variation due to different semiconductor processes, but not much. For example, the reference voltage Vref possibly varies between 1.17V˜1.37V when Vf10 is 0.5V˜0.7V.
However, one of the shortcomings of the bandgap reference circuit in the prior arts is that the bandgap reference circuit can not normally operate if the power source Vcc is less than the reference Vref, such as 1.27V, because the differential operational amplifier OP and the MOS P do not properly work.
For further illustration, please refer to another example in the prior arts as shown in FIG. 2. Similar to the structure in FIG. 1, the bandgap reference circuit in FIG. 2 generally comprises a differential operational amplifier OP, a first transistor P1, a second transistor P2, a third transistor P3, a first resistor R1, a second resistor R2, a third resistor R3, a fourth resistor R4, a first diode D1 and a second diode D2. The second diode D2 is implemented by several diodes connected in parallel and each identical to the first diode D1 in electrical property.
Specifically, the output end of the differential operational amplifier OP is connected to the gate terminals of the first transistor P1, the second transistor P2 and the third transistor P3, the source terminals of the a first transistor P1, the second transistor P2 and the third transistor P3 are connected to the power source Vcc. The positive end of the first diode D1 and one end of the first resistor R1 are connected to the drain terminal of the first transistor P1. One end of the second resistor R2 and one end of the third resistor R3 are connected to the drain terminal of the second transistor P2, the other end of the third resistor R3 is connected to the positive end of the second diode D2, and one end of the fourth resistor R4 is connected to the drain terminal of the third transistor P3. Furthermore, the other end of the first resistor R1, the negative end of the first diode D1, the negative end of the second diode D2, the other end of the second resistor R2 and the other end of the fourth resistor R4 are grounded.
Particularly, the drain terminal of the first transistor P1 is further connected to the inverting input end of the differential operational amplifier OP, and the drain terminal of the second transistor P2 is further connected to the non-inverting input end of the differential operational amplifier OP, thereby providing feedback control loop and the reference voltage Vref at the drain terminal of the third transistor P3.
Hereafter, the operation of the bandgap reference circuit in FIG. 2 will be described in detail.
Each of the transistors P1, P2 and P3 has identical electrical property such that the inverting input voltage Va is equal to the non-inverting input voltage Vb when the differential operational amplifier OP is operated at the steady state, that is, I1a=I2a and I1b=I2b, where the current I1a flows through the first diode D1, the current I2a flows through the third resistor R3, the current I1b flows through the first resistor R1, and the current I2b flows through the second resistor R2. Therefore, the following equation (9) is obtained:
                                                                        d                ⁢                                                                  ⁢                Vf                            =                            ⁢                                                Vf                  ⁢                                                                          ⁢                  1                                -                                  Vf                  ⁢                                                                          ⁢                  2                                                                                                        =                            ⁢                                                V                  T                                ·                                  In                  ⁡                                      (                                                                                            N                          ·                          I                                                ⁢                                                                                                  ⁢                        1                        ⁢                        a                                                                    I                        ⁢                                                                                                  ⁢                        2                        ⁢                        a                                                              )                                                                                                                          =                            ⁢                                                V                  T                                ·                                                      In                    ⁡                                          (                      N                      )                                                        .                                                                                        (        9        )            
And, the reference voltage Vref can be expressed as equation (10):
                                                        Vref              =                            ⁢                              R                ⁢                                                                  ⁢                                  4                  ·                  I                                ⁢                                                                  ⁢                3                                                                                        =                            ⁢                              R                ⁢                                                                  ⁢                                  4                  ·                                      (                                                                  I                        ⁢                                                                                                  ⁢                        2                        ⁢                        b                                            +                                              I                        ⁢                                                                                                  ⁢                        2                        ⁢                        a                                                              )                                                                                                                          =                            ⁢                              R                ⁢                                                                  ⁢                                  4                  ·                                      (                                                                                            Vf                          ⁢                                                                                                          ⁢                          1                                                                          R                          ⁢                                                                                                          ⁢                          2                                                                    +                                                                        d                          ⁢                                                                                                          ⁢                          Vf                                                                          R                          ⁢                                                                                                          ⁢                          3                                                                                      )                                                                                                                                                            =                                    ⁢                                                                                    R                        ⁢                                                                                                  ⁢                        4                                                                    R                        ⁢                                                                                                  ⁢                        2                                                              ·                                          [                                                                        Vf                          ⁢                                                                                                          ⁢                          1                                                +                                                                              (                                                                                          R                                ⁢                                                                                                                                  ⁢                                2                                                                                            R                                ⁢                                                                                                                                  ⁢                                3                                                                                      )                                                    ·                          dVf                                                                    )                                                                      ]                            .                                                          (        10        )            
Moreover, equation (11) is thus derived from equations (4) and (8):
                                          [                                          Vf                ⁢                                                                  ⁢                1                            +                                                (                                                            R                      ⁢                                                                                          ⁢                      2                                                              R                      ⁢                                                                                          ⁢                      3                                                        )                                ·                dVf                                      )                    ]                =                  1.27          .                                    (        11        )            
At this time, equation (11) is put into equation (10) to acquire the reference voltage Vref as shown by equation (12):
                    Vref        =                                            R              ⁢                                                          ⁢              4                                      R              ⁢                                                          ⁢              2                                ×                      1.27            .                                              (        12        )            
Therefore, the reference voltage Vref is changed by adjusting the ratio of R4/R2 such that the bandgap reference circuit can still properly function at the power source Vcc less than 1.27V.
However, the shortcoming of the above bandgap reference circuit is that if R1=R2 and Va and Vb do not attain the corresponding cut-in voltage Vth of the diodes D1 and D2, respectively, at the beginning of starting, I1b>>I1a and I2b>>I1a such that Va is almost equal to Vb, and the differential operational amplifier OP does not normally work. Thus, start failure results. Another problem is that the bandgap reference circuit has more than one stable operating point, that is, several intersection points of the inverting input voltage Va and the non-inverting input voltage Vb, as shown in FIG. 3. More specifically, the bandgap reference circuit can normally perform at the stable operating point A. But, the bandgap reference circuit fails at the multiple stable operating points B, that is, the points when the inverting input voltage Va and the non-inverting input voltage Vb are the same. This is because the bandgap reference circuit may perform at the stable operating points B before the inverting input voltage Va and the non-inverting input voltage Vb attain the corresponding cut-in voltage Vth of the diodes D1 and D2, respectively. Consequently, the whole electrical function of the bandgap reference circuit fails.
Therefore, it is greatly needed for a low voltage bandgap reference circuit, which is able to adjust the reference voltage generated and has a single stable operating point less than the power source so as to avoid the start failure at low voltage, thereby solving the above problems of the bandgap reference circuit in the prior arts.